Some help with a stats question?

[Lord Ash]

Okay guys, help me out with a disagreement...

This is somewhat hypothetical, but I'd appreciate your input.

Let's say you have two basketball players.

One played 1600 games. (Again, this is somewhat theoretical, so ignore that the numbers are huge)

One played 4000 games.

They played literally the exact same minutes per game in every game, played with the exact same teammates, and played against the exact same level of competition.

Neither one got older or younger or anything; age played no role in their stats (this is, again, theoretical).

Can you compare their per game stats in some meaningful way, since they played the same number of minutes and the stats are per game? Or does the fact that the one guy played more games somehow make the stats unable to be compared? Like.. could you compare their assists per game in any meaningful way, or does the one player playing more invalidate comparisons? If the raw number of games DOES make it impossible to compare them, how does it?

Thanks guys and gals!:)

[rthomas]

Okay guys, help me out with a disagreement...

This is somewhat hypothetical, but I'd appreciate your input.

Let's say you have two basketball players.

One played 1600 games. (Again, this is somewhat theoretical, so ignore that the numbers are huge)

One played 4000 games.

They played literally the exact same minutes per game in every game, played with the exact same teammates, and played against the exact same level of competition.

Neither one got older or younger or anything; age played no role in their stats (this is, again, theoretical).

Can you compare their per game stats in some meaningful way, since they played the same number of minutes and the stats are per game? Or does the fact that the one guy played more games somehow make the stats unable to be compared? Like.. could you compare their assists per game in any meaningful way, or does the one player playing more invalidate comparisons? If the raw number of games DOES make it impossible to compare them, how does it?

Thanks guys and gals!:)

The number of games doesn't matter - you may still compare them.

[JasonEvans]

Well, "can you compare..." is subjective. I mean, of course you can compare them. I'm not really clear what you are asking here. Are you asking if one set of stats are more accurate or predictive of player production than the other?

The basic answer is that as your sample size gets larger and larger, random variance gets to be less and less. In other words the predictive (and descriptive) value of your stats are increasingly accurate. So, in the case of your example, we are better able to predict the performance of the guy with 4000 games of data versus the player with 1600 games.

But, that increased predictive ability comes at a diminishing rate as we accumulate more and more data. If you were asking about the value of stats on someone who played 5 or 10 or 50 or even 100 games, I would say that several thousand games of data would be perhaps significantly more accurate. But, in your example, we have someone who played 1600 games. That't a ton of data. A lot of "random statistical variance" gets ironed out when you get to that large of a data set. I'm not sure there is a truly meaningful difference in the quality of a 4000 game data set versus a 1600 game set. I suppose a statistician might be able to say the 4000 game set is 0.05% more accurate (or something like that) but I'm not sure that difference is all that significant. I guess it depends on what you wanted to measure.

-Jason "does that make sense?" Evans

[Lord Ash]

Hi guys,

Sure Jason, makes total sense.

This came about as two people were debating which player was a more willing passer, and it was pointed out that they have the same assists per game.

Someone said "Yeah, but that guy has 4000 games played, that other guy has 1600, you cannot compare them, because the one guy played so much more." There was no math point made to back that up.

Someone else said "Of course you can compare them; those are pretty big data sets, and given that it is adjusted for minutes and games and all of that, sure you can."

I am of the mind that obviously you can compare them, given that the minutes per game are the same, the teammates are the same, the competition was the same, and they both played enough games to iron out the occasional extreme result. That seemed obvious to me, but there was some pushback.

[gus]

Okay guys, help me out with a disagreement...

This is somewhat hypothetical, but I'd appreciate your input.

Let's say you have two basketball players.

One played 1600 games. (Again, this is somewhat theoretical, so ignore that the numbers are huge)

One played 4000 games.

They played literally the exact same minutes per game in every game, played with the exact same teammates, and played against the exact same level of competition.

Neither one got older or younger or anything; age played no role in their stats (this is, again, theoretical).

Can you compare their per game stats in some meaningful way, since they played the same number of minutes and the stats are per game? Or does the fact that the one guy played more games somehow make the stats unable to be compared? Like.. could you compare their assists per game in any meaningful way, or does the one player playing more invalidate comparisons? If the raw number of games DOES make it impossible to compare them, how does it?

Thanks guys and gals!:)

The confidence interval (https://www.mathsisfun.com/data/confidence-interval.html) will tighten with more games, but the difference isn't appreciable from 1600 to 4000, so yes, you can draw meaningful comparisons between those two datasets.

[BD80]

... yes, you can draw meaningful comparisons between those two datasets.

But I'd recommend drawing with pencil with an eraser. Does wonders for my golf game - statistically speaking.

[cspan37421]

averages from 16 games vs. 40 games would be less comparable than averages from 1600 vs. 4000.

If you chose those huge numbers to obscure what you were really looking at, then your intuition about the average may not apply to the real figures you're considering.

[Lord Ash]

averages from 16 games vs. 40 games would be less comparable than averages from 1600 vs. 4000.

If you chose those huge numbers to obscure what you were really looking at, then your intuition about the average may not apply to the real figures you're considering.

No no, those are actual literal numbers of games played, not an extrapolation or exaggerated number to obscure intent. Seems strange, but...

[rthomas]

There are statistical tests specifically for comparing populations with uneven sample sizes, which breaks an assumption (if unequal variances) of other statistical tests.

[CDu]

It really depends on the question, the numbers, and how numbers differ over time. Are the games played at comparable stages of one’s life, or did one player play his games all in his prime versus another well before or after his prime? And does that matter to the question itself?

Statistically speaking, there is a point at which the sample is large enough that - assuming observations are otherwise “similar enough” - you can be pretty confident in their estimates. 1600 and 4000 games certainly fall oin that category hypothetically. But in practice, I would guess that the player with 4000 games had plenty of games that aren’t comparable (due to age).

[Lord Ash]

It really depends on the question, the numbers, and how numbers differ over time. Are the games played at comparable stages of one’s life, or did one player play his games all in his prime versus another well before or after his prime? And does that matter to the question itself?

Statistically speaking, there is a point at which the sample is large enough that - assuming observations are otherwise “similar enough” - you can be pretty confident in their estimates. 1600 and 4000 games certainly fall oin that category hypothetically. But in practice, I would guess that the player with 4000 games had plenty of games that aren’t comparable (due to age).

Hey CDu!

From the original...

They played literally the exact same minutes per game in every game, played with the exact same teammates, and played against the exact same level of competition.

Neither one got older or younger or anything; age played no role in their stats (this is, again, theoretical).

Just FYI, this are computer game numbers; the question was specifically "Does the fact that these two players have the same assists per game mean that you can assume they are reasonably similar in terms of effective passing to teammates?"

[Mtn.Devil.91.92.01.10.15]

Hey CDu!

From the original...

They played literally the exact same minutes per game in every game, played with the exact same teammates, and played against the exact same level of competition.

Neither one got older or younger or anything; age played no role in their stats (this is, again, theoretical).

Just FYI, this are computer game numbers; the question was specifically "Does the fact that these two players have the same assists per game mean that you can assume they are reasonably similar in terms of effective passing to teammates?"

Okay, I will pipe up.

What is the goal? Just ranking the two? Ranking their overall careers? Picking the most reliable player for your team?

Or is this simply a math exercise?

[CDu]

Hey CDu!

From the original...

They played literally the exact same minutes per game in every game, played with the exact same teammates, and played against the exact same level of competition.

Neither one got older or younger or anything; age played no role in their stats (this is, again, theoretical).

Just FYI, this are computer game numbers; the question was specifically "Does the fact that these two players have the same assists per game mean that you can assume they are reasonably similar in terms of effective passing to teammates?"

Doh! Diligent reading on Friday afternoons is apparently not a strong suit of mine. :/

Ignoring other things (like turnovers), and assuming all else constant, yeah, you have a sufficient sample size to make reasonable comparisons on things like assists per game. As has been mentioned by others, there are significance tests that could give you a confidence interval around each mean to give you a truly mathematical interpretation of the differences. But from a layman's perspective, 1600 is certainly a big enough sample to feel confident in discussing something as common as assists per game.

If it was, say, 10 games versus 4000, you would have to have a HUGE difference in the means to confidently say anything about one being better than the other.

But I'd still caveat that it really depends on the exact question of interest, and the data point(s) of focus.

[Lord Ash]

Hey guys!

Yeah, what it really came down to is two players arguing... one accused the other of not passing the ball much, but the other pointed out they had the same assists per game, so that seems a bit odd to say. I tend to think that the sample size is just so huge that yes, assists per game is a decent metric (and in fact the ONLY actual, non-eye-test metric) you can look at for that sort of thing.

[PackMan97]

No you can't compare.

I suspect one of these players in a Tarcheat and therefore had unfair advantages the other player didn't have.

[left_hook_lacey]

As Jason and Gus said, with that large of a data set, the difference in confidence interval would be minimal, I think.

There are hypothetical tests you can plug in to statistical software like I use at work, and it will tell you how many samples you need to be able to predict with a >95% confidence interval, which is the golden number for predicting future performance, or as it sounds in this case, "who was better".

I can tell you that in most of the exercises I've done, 1,600 samples is more than enough to establish a reliable confidence interval. Sure, 4,000 or whatever it was, is better, but not enough to say you can't compare the two.


Who are the two players? I'm nerdily interested now, and would be willing to plug in the stats of both players(for assists?) and see what the difference in the confidence intervals would be and go from there.

[Lord Ash]

Hey!

Okay... so, don't laugh, but it was a video game argument... namely NBA 2k17. I play as a big center, and a shooting guard I normally play with accused me of being a bit of a ball hog. I was like "No I'm not!" and he insisted I was. I then pointed out that my center has the same assists per game as his guard. He went on about how you can't compare us because he played more games. I kept trying to get him to point out mathematically how it mattered; he was unable to, but accused me of not understanding stats.

Accuse me of being a ball hog, and then accuse me of not understanding stats? OHHHH no no no, you SOB!:)

[left_hook_lacey]

Hey!

Okay... so, don't laugh, but it was a video game argument... namely NBA 2k17. I play as a big center, and a shooting guard I normally play with accused me of being a bit of a ball hog. I was like "No I'm not!" and he insisted I was. I then pointed out that my center has the same assists per game as his guard. He went on about how you can't compare us because he played more games. I kept trying to get him to point out mathematically how it mattered; he was unable to, but accused me of not understanding stats.

Accuse me of being a ball hog, and then accuse me of not understanding stats? OHHHH no no no, you SOB!:)

Well, without doing a lot of work, you could also point out that it's even harder for a center to get the same apg as a guard, because a center's ball handling and passing attributes are way lower, they don't get dimer badges, etc. Yeah, I play 2k18, but the argument is the same.


What type of guard is his build? What type of center is yours? Just curious.

[Lord Ash]

Oh dude, totally. Oh, and sorry, we play 18, not 17:)

And we ONLY play Park, so I cannot get an assist by getting the ball on an inbounds play after an opponent made bucket and then passing it up to someone for a bucket, because I am always passing the ball in... and rarely can I get it off an "inbound" play on their side of the court, because I find that guards make that initial pass to other guards 99 percent of the time, not to a big.

I was a rebounding post scorer, but switched to a two way athletic finisher. He has several characters, but his primary were a slashing shot creator and a playmaking sharpshooter.

And the worst part is that he is a bit of a ball hog, so I was really offended:)

[left_hook_lacey]

Oh dude, totally. Oh, and sorry, we play 18, not 17:)

And we ONLY play Park, so I cannot get an assist by getting the ball on an inbounds play after an opponent made bucket and then passing it up to someone for a bucket, because I am always passing the ball in... and rarely can I get it off an "inbound" play on their side of the court, because I find that guards make that initial pass to other guards 99 percent of the time, not to a big.

I was a rebounding post scorer, but switched to a two way athletic finisher. He has several characters, but his primary were a slashing shot creator and a playmaking sharpshooter.

And the worst part is that he is a bit of a ball hog, so I was really offended:)

Ha ha. Understood.

What's ya'lls overalls on the ones you play with the most?

I have a 90 overall two-way rebounder, but I made him too small. Now I play with a rebounding stretch 5, who should hit 91 overall this week if I play. Haven't played since last week because I was at the beach.

[Lord Ash]

My top guy (post scoring rebounder) is a 92. My new guy is an 88. The crew I play with is all between 91 and 96 I think?

A stretch big. I hate you. If you want to shoot threes, create a damn guard.

;)

[left_hook_lacey]

My top guy (post scoring rebounder) is a 92. My new guy is an 88. The crew I play with is all between 91 and 96 I think?

A stretch big. I hate you. If you want to shoot threes, create a damn guard.

;)

Get with the times man! Centers don't hang out under the rim anymore! :cool:

Seriously though, my guy is rebounding primary, shooting secondary, so he has the lowest shooting attributes of any stretch big. He's also 7' 3", so he has to be wide open to get a good shot. I NEVER take bad 3's. And really, the only time I hang out around the 3 point line is if I have a glass cleaner or lock down defender guarding me to keep them out of the paint and let someone else take advantage of the open lane.

And conversely, if I have a smaller center or forward guarding me, I'll post them up, then kick it out to the best shooter on our team, then crash the board for the rebound with my REBOUNDING stretch 5! :)

I don't play park as much as you. I'd say I play it about 33.3% of the time between MyCareer, Pro-am, and Park. My record is not good because this is my first year playing and had no idea about the whole park element and frankly, didn't realize how important the rankings were. I literally lost 36 games in a row right after I bought the game because I was a 60, and would play with any garbage that stepped on the spot against 90+'s. At the time, I didn't think I would keep playing park and didn't really care about the record. Once I started getting better, I started taking my record more seriously and have started being very selective of who I play with.

I have a couple of guys that I play with now that are really good, but they're a lot younger than me, so they can get annoying sometimes when they start arguing with each other, or we'll go on a streak and they'll start taking half-court 3's playing around. I can't stand that. I want to beat everyone 21-0.

If you want, send me your name and we can play together sometime. If you've played 1,600 games, and your teammate has played 4,000+, I'd be willing to bet we've crossed paths before.

[left_hook_lacey]

Get with the times man! Centers don't hang out under the rim anymore! :cool:

Seriously though, my guy is rebounding primary, shooting secondary, so he has the lowest shooting attributes of any stretch big. He's also 7' 3", so he has to be wide open to get a good shot. I NEVER take bad 3's. And really, the only time I hang out around the 3 point line is if I have a glass cleaner or lock down defender guarding me to keep them out of the paint and let someone else take advantage of the open lane.

And conversely, if I have a smaller center or forward guarding me, I'll post them up, then kick it out to the best shooter on our team, then crash the board for the rebound with my REBOUNDING stretch 5! :)

I don't play park as much as you. I'd say I play it about 33.3% of the time between MyCareer, Pro-am, and Park. My record is not good because this is my first year playing and had no idea about the whole park element and frankly, didn't realize how important the rankings were. I literally lost 36 games in a row right after I bought the game because I was a 60, and would play with any garbage that stepped on the spot against 90+'s. At the time, I didn't think I would keep playing park and didn't really care about the record. Once I started getting better, I started taking my record more seriously and have started being very selective of who I play with.

I have a couple of guys that I play with now that are really good, but they're a lot younger than me, so they can get annoying sometimes when they start arguing with each other, or we'll go on a streak and they'll start taking half-court 3's playing around. I can't stand that. I want to beat everyone 21-0.

If you want, send me your name and we can play together sometime. If you've played 1,600 games, and your teammate has played 4,000+, I'd be willing to bet we've crossed paths before.

I take that as a no.

[CDu]

LOL, a message board statistics discussion about video game stats. It doesn’t get much nerdier than that. :)

And I say that in full humor/self-deprecation mode, as I was all-in on the statistics discussion and own my nerdiness. :)

[left_hook_lacey]

LOL, a message board statistics discussion about video game stats. It doesn’t get much nerdier than that. :)

And I say that in full humor/self-deprecation mode, as I was all-in on the statistics discussion and own my nerdiness. :)

The word Nerdvana comes to mind. 😀

[Lord Ash]

Oh sorry, Left! I missed your post! You on Xbox, or PS?

[left_hook_lacey]

Oh sorry, Left! I missed your post! You on Xbox, or PS?

I'm on PS4.

[Lord Ash]

Aw crap. Xbone:(

[left_hook_lacey]

Aw crap. Xbone:(

That's a shame.